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Volumn 26, Issue 2, 2001, Pages 233-244

An optimal deterministic algorithm for computing the diameter of a three-dimensional point set

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EID: 0035634204     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00454-001-0029-8     Document Type: Article
Times cited : (28)

References (37)
  • 2
    • 51249167141 scopus 로고
    • On range searching with semialgebraic sets
    • P. K. Agarwal and J. Matoušek. On range searching with semialgebraic sets. Discrete Comput. Geom. 11 (1994), 393-418.
    • (1994) Discrete Comput. Geom. , vol.11 , pp. 393-418
    • Agarwal, P.K.1    Matoušek, J.2
  • 5
    • 0033902897 scopus 로고    scopus 로고
    • Computing the arrangement of curve segments: Divide-and-conquer algorithms via sampling
    • Manuscript
    • N. M. Amato, M. T. Goodrich, and E. A. Ramos. Computing the Arrangement of Curve Segments: Divide-and-Conquer Algorithms via Sampling. Manuscript, 1999. Short abstract in Proc. 9th Annu. ACM-SIAM Sympos. Discrete Algorithms (SODA 00), pp. 705-706, 2000. Available from http:// www.mpi-sb.mpg.de/∼ramos
    • (1999) Proc. 9th Annu. ACM-SIAM Sympos. Discrete Algorithms (SODA 00) , pp. 705-706
    • Amato, N.M.1    Goodrich, M.T.2    Ramos, E.A.3
  • 9
    • 33244480878 scopus 로고
    • A deterministic view of random sampling and its use in geometry
    • B. Chazelle and J. Friedman. A deterministic view of random sampling and its use in geometry. Combinatorica, 10 (1990) 229-249.
    • (1990) Combinatorica , vol.10 , pp. 229-249
    • Chazelle, B.1    Friedman, J.2
  • 10
    • 0024054715 scopus 로고
    • A randomized algorithm for closest-point queries
    • K. L. Clarkson. A randomized algorithm for closest-point queries. SIAM J. Comput. 17 (1988), 830-847.
    • (1988) SIAM J. Comput. , vol.17 , pp. 830-847
    • Clarkson, K.L.1
  • 11
    • 0001702902 scopus 로고
    • Applications of random sampling in computational geometry, II
    • K. L. Clarkson and P. W. Shor. Applications of random sampling in computational geometry, II. Discrete Comput. Geom. 4 (1989), 387-421.
    • (1989) Discrete Comput. Geom. , vol.4 , pp. 387-421
    • Clarkson, K.L.1    Shor, P.W.2
  • 13
    • 0039223943 scopus 로고    scopus 로고
    • A randomized algorithm for the Voronoi diagram of line segments on coarse grained multiprocessors
    • X. Deng and B. Zhu. A randomized algorithm for the Voronoi diagram of line segments on coarse grained multiprocessors. Algorithmica 24 (1999), 270-286.
    • (1999) Algorithmica , vol.24 , pp. 270-286
    • Deng, X.1    Zhu, B.2
  • 14
    • 0001520324 scopus 로고
    • Fast detection of polyhedral intersection
    • D. P. Dobkin and D. G. Kirkpatrick. Fast detection of polyhedral intersection. Theoret. Comput. Sci. 27 (1983), 241-253.
    • (1983) Theoret. Comput. Sci. , vol.27 , pp. 241-253
    • Dobkin, D.P.1    Kirkpatrick, D.G.2
  • 16
    • 0025214884 scopus 로고
    • Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms
    • H. Edelsbrunner and E. P. Mücke. Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms. ACM Trans. Graph. 9 (1990), 66-104.
    • (1990) ACM Trans. Graph. , vol.9 , pp. 66-104
    • Edelsbrunner, H.1    Mücke, E.P.2
  • 17
    • 0012042657 scopus 로고    scopus 로고
    • Efficient perturbations for handling geometric degeneracies
    • I. Z. Emiris, J. F. Canny and R. Seidel. Efficient perturbations for handling geometric degeneracies. Algorithmica 19 (1997), 219-242.
    • (1997) Algorithmica , vol.19 , pp. 219-242
    • Emiris, I.Z.1    Canny, J.F.2    Seidel, R.3
  • 18
    • 0029512809 scopus 로고
    • Planar separators and parallel polygon triangulation
    • M. T. Goodrich. Planar separators and parallel polygon triangulation. J. Comput. System Sci. 51 (1995), 374-389.
    • (1995) J. Comput. System Sci. , vol.51 , pp. 374-389
    • Goodrich, M.T.1
  • 19
    • 0031522631 scopus 로고    scopus 로고
    • Bounded independence derandomization of geometric partitioning with applications to parallel fixed-dimensional linear programming
    • M. T. Goodrich and E. A. Ramos. Bounded independence derandomization of geometric partitioning with applications to parallel fixed-dimensional linear programming. Discrete Comput. Geom. 18 (1997), 397-420.
    • (1997) Discrete Comput. Geom. , vol.18 , pp. 397-420
    • Goodrich, M.T.1    Ramos, E.A.2
  • 20
    • 15744365331 scopus 로고
    • Epsilon-nets and simplex range queries
    • D. Haussler and E. Welzl. Epsilon-nets and simplex range queries. Discrete Comput. Geom. 2 (1987), 127-151.
    • (1987) Discrete Comput. Geom. , vol.2 , pp. 127-151
    • Haussler, D.1    Welzl, E.2
  • 21
    • 0040408333 scopus 로고
    • Beweis einer Vermutung von A. Vázsonyi
    • A. Heppes. Beweis einer Vermutung von A. Vázsonyi. Acta Math. Acad. Sci. Hungar. 7 (1956), 463-466.
    • (1956) Acta Math. Acad. Sci. Hungar. , vol.7 , pp. 463-466
    • Heppes, A.1
  • 23
    • 0018457301 scopus 로고
    • A separator theorem for planar graphs
    • R. J. Lipton and R. E. Tarjan. A separator theorem for planar graphs. SIAM J. Comput. 36 (1979), 177-189.
    • (1979) SIAM J. Comput. , vol.36 , pp. 177-189
    • Lipton, R.J.1    Tarjan, R.E.2
  • 24
    • 85031734140 scopus 로고
    • Approximations and optimal geometric divide-and-conquer
    • J. Matoušek. Approximations and optimal geometric divide-and-conquer. In Proc. 23rd Annu. ACM Sympos. Theory Comput. (STOC 91), pp. 505-511, 1991. Also in J. Comput. System Sci. 50, 203-208 (1995).
    • (1991) Proc. 23rd Annu. ACM Sympos. Theory Comput. (STOC 91) , pp. 505-511
    • Matoušek, J.1
  • 25
    • 0029293361 scopus 로고
    • J. Matoušek. Approximations and optimal geometric divide-and-conquer. In Proc. 23rd Annu. ACM Sympos. Theory Comput. (STOC 91), pp. 505-511, 1991. Also in J. Comput. System Sci. 50, 203-208 (1995).
    • (1995) J. Comput. System Sci. , vol.50 , pp. 203-208
  • 26
    • 21144462806 scopus 로고
    • Efficient partition trees
    • J. Matoušek. Efficient partition trees Discrete Comput. Geom. 8 (1992), 315-334.
    • (1992) Discrete Comput. Geom. , vol.8 , pp. 315-334
    • Matoušek, J.1
  • 27
    • 0030364522 scopus 로고    scopus 로고
    • Derandomization in computational geometry
    • J. Matoušek. Derandomization in computational geometry. J. Algorithms 20 (1996), 545-580.
    • (1996) J. Algorithms , vol.20 , pp. 545-580
    • Matoušek, J.1
  • 28
    • 0027313812 scopus 로고
    • A deterministic algorithm for the three-dimensional diameter problem
    • J. Matoušek and O. Schwarzkopf. A deterministic algorithm for the three-dimensional diameter problem. In Proc. 25th Annu. ACM Sympos. Theory Comput. (STOC 93), pp. 478-484, 1993. Revised version in Comput. Geom. Theory Appl. 6 (1996), 253-262.
    • (1993) Proc. 25th Annu. ACM Sympos. Theory Comput. (STOC 93) , pp. 478-484
    • Matoušek, J.1    Schwarzkopf, O.2
  • 29
    • 0009891842 scopus 로고    scopus 로고
    • J. Matoušek and O. Schwarzkopf. A deterministic algorithm for the three-dimensional diameter problem. In Proc. 25th Annu. ACM Sympos. Theory Comput. (STOC 93), pp. 478-484, 1993. Revised version in Comput. Geom. Theory Appl. 6 (1996), 253-262.
    • (1996) Comput. Geom. Theory Appl. , vol.6 , pp. 253-262
  • 34
    • 0001024505 scopus 로고
    • On the uniform convergence of relative frequencies of events to their probabilities
    • V. N. Vapnik and A. Y. Chervonenkis. On the uniform convergence of relative frequencies of events to their probabilities. Theory Probab. Appl. 16 (1971), 264-280.
    • (1971) Theory Probab. Appl. , vol.16 , pp. 264-280
    • Vapnik, V.N.1    Chervonenkis, A.Y.2
  • 35
    • 0001154535 scopus 로고
    • On constructing minimum spanning trees in k-dimensional space and related problems
    • A. C. Yao. On constructing minimum spanning trees in k-dimensional space and related problems. SIAM J. Comput. 11 (1982), 721-736.
    • (1982) SIAM J. Comput. , vol.11 , pp. 721-736
    • Yao, A.C.1
  • 37
    • 0039815838 scopus 로고
    • A geometric consistency theorem for a symbolic perturbation scheme
    • C. K. Yap. A geometric consistency theorem for a symbolic perturbation scheme. J. Comput. System Sci. 39 (1989), 236-246.
    • (1989) J. Comput. System Sci. , vol.39 , pp. 236-246
    • Yap, C.K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.